A system of equations | Algebra homework help

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<object:standard:macc.912.a–rei.3.5>A system of equations is shown below:

x + 3y = 5      (equation 1)
7x – 8y = 6     (equation 2)

A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?

 


 

 

Question 2 

 

(05.02)<object:standard:macc.912.a–rei.3.6>

Solve the following system of equations:
3x – 2y = 6
6x – 4y = 12

 


 

 

Question 3 

 

(05.01)<object:standard:macc.912.a–rei.3.6>

Which graph below shows a system of equations with infinitely many solutions?

 


 

 

Question 4 

 

(05.02)<object:standard:macc.912.a–rei.3.6>

A system of equations is shown below:

x + y = 3
2x – y = 6

The x-coordinate of the solution to this system of equations is _____.

Numerical Answers Expected!

Answer for Blank 1:

 


 

 

Question 6 

 

(05.06)<object:standard:macc.912.a–ced.1.3>

Nick works two jobs to pay for college. He tutors for $15 per hour and also works as a bag boy for $8 per hour. Due to his class and study schedule, Nick is only able to work up to 20 hours per week but must earn at least $150 per week. If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?

 


 

 

Question 7 

 

(05.02)<object:standard:macc.912.a–rei.3.5>

Two systems of equations are shown below:

System A

System B

2x + y = 5

-10x + 19y = -1

-4x + 6y = -2

-4x + 6y = -2

Which of the following statements is correct about the two systems of equations?

 

 


 

 

Question 8 

 

(05.06)<object:standard:macc.912.a–rei.4.12>

A system of linear inequalities is shown below:

y – x > 0
x + 1 < 0

Which of the following graphs best represents the solution set to this system of linear inequalities?

 


 

 

Question 9 

 

(05.02)<object:standard:macc.912.a–rei.3.6>

The total price of a shirt and a cap is $11. If the price of the shirt was doubled and the price of the cap was 3 times its original price, the total price of a shirt and a cap would be $25. What is the price of a shirt and a cap?

 


 

 

Question 10 

 

(05.05)<object:standard:macc.912.a–rei.4.12>

Select the inequality that corresponds to the given graph. 

graph with a y–intercept at 0 comma 1 and a second point at 4 comma 2. This is a dashed line with shading above the line

 


 

 

Question 11 

 

(05.03)<object:standard:macc.912.a–rei.4.10>

The graph of an equation is shown below:

line joining ordered pairs negative 3,2 and 1, negative 2

Based on the graph, which of the following represents a solution to the equation?

 


 

 

Question 12 

 

(05.03)<object:standard:macc.912.a–rei.4.11>

The tables below show the values of f(x) and g(x) for different values of x:

f(x) = 2(3)x 

g(x) = 3x + 9

x g(x)
-2 9.11
-1 9.33
0 10
1 12
2 18

Based on the tables, what is the solution to the equation 2(3)x = 3x + 9?

 

 


 

 

Question 13 

 

(05.03)<object:standard:macc.912.a–rei.4.11>

An equation is shown below:

2 over 3 multiplied by x plus 8 over 3 equals 2 to the power of x

What is the solution to the equation?

 


 

 

Question 14 

 

(05.02)<object:standard:macc.912.a–ced.1.3>

Maya had $27. She spent all the money on buying 3 burgers for $x each and 2 sandwiches for $y each. If Maya had bought 2 burgers and 1 sandwich, she would have been left with $11. 

A student concluded that the price of each burger is $5 and the price of each sandwich is $6. Which statement best justifies whether the student’s conclusion is correct or incorrect?

 


 

 

Question 15 

 

(05.06)<object:standard:macc.912.a–rei.4.12>

Look at the graph below:

First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3

Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ –1?

 


 

 

Question 16 

 

(05.05)<object:standard:macc.912.a–rei.4.12>

A graph is shown below:

solid line joining ordered pair 0, 0 and 8, 5 and the region below this line which lies in the first quadrant is shaded

Which of the following inequalities is best represented by this graph?

 


 

 

Question 17 

 

(05.01)<object:standard:macc.912.a–rei.3.6>

The graph plots four equations, A, B, C, and D:

Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7.

Which pair of equations has (0, 8) as its solution?

 


 

 

Question 18 

 

(05.03)<object:standard:macc.912.a–rei.4.11>

The graph below shows two functions:

function f of x is a straight line which joins the ordered pairs negative 3.5, 15 and 4, 0. Function g of x is a curved line which joins the ordered pairs negative 1.7, 11.5 and 4, 0

Based on the graph, what are the approximate solutions to the equation –2x + 8 = (0.25)x?

 


 

 

Question 19 

 

(05.05)<object:standard:macc.912.a–rei.4.12>

Greg made 4 chairs and 3 tables. Greg only has enough plywood to make at most 15 chairs or tables total. Let x represent the number of more chairs and y represent the number of more tables that Greg can make. Which of the following graphs best represents the relationship between x and y?

 


 

 

Question 20 

 

(05.02)<object:standard:macc.912.a–rei.3.6>

For the following system, if you isolated x in the first equation to use the Substitution Method, what expression would you substitute into the second equation?

-x – 2y = -4
3x + y = 12

 


 

 

Question 21

 

(05.05)<object:standard:macc.912.a–rei.4.12>

Sally has only nickels and dimes in her money box. She knows that she has less than $20 in the box. Let x represent the number of nickels in the box and y represent the number of dimes in the box. Which of the following statements best describes the steps to graph the solution to the inequality in x and y?

 


 

 

Question 22 

 

(05.03)<object:standard:macc.912.a–rei.4.10>

Which of the following statements best describes the graph of –5x + 2y = 1?

 


 

 

Question 23 

 

(05.01)<object:standard:macc.912.a–rei.3.6>

A pair of linear equations is shown below:

y = –x + 1
y = 2x + 4

Which of the following statements best explains the steps to solve the pair of equations graphically?